List of top Mathematics Questions on Linear Programmig Problem

Consider the following feasible region. Which of the following constraints represents the feasible region ?

A. 2x + 3y ≤ 6
B. x - 2y ≤ 2
C. 3x + 2y ≤ 12
D. 3x - 2y ≤ -3
E. x - 2y ≥ -1
Choose the correct answer from the options given below :

Match List I with List II

List I	List II
A. The region represented by \(x \geq 0, y \geq 0\)	I. no feasible region
B. The region represented by the inequalities \(2x + y \geq 3, x + 2y \geq 6, x,y \geq 0\)	II. 1st quadrant
C. The region represented by the inequalities \(x + 2y \leq 8, 3x + 2y \leq 12, x,y \geq 0\)	III. unbounded
D. The region represented by the inequalities \(x + y \leq 2, 3x + 5y \geq 15, x,y \geq 0\)	IV. bounded

Choose the correct answer from the options given below:

If corner points of a feasible region are (0, 0), (2,0) \((\frac{20}{19},\frac{45}{19})\) and (0, 3), then
(A) Maximum value of z=5x+3y is 10
(B) Minimum value of z=5x+3y is 0
(C) Maximum value of z=5x+3y is \(\frac{235}{19}\) and minimum value is 0
(D) Maximum value of z=5x+3y is 10 and minimum value is 0
Choose the correct answer from the options given below :

The value of objective function is maximum under linear constraints is

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then

For the problem max Z = ax + by, x≥0, y ≥0, which of the following is NOT a valid constraint to make it a linear programming problem?

Choose the wrong statement from the following:

A carpenter earns a profit of ₹50 and ₹80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as:

The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively:

An electric company has 300 Transistors, 400 Capacitors and 500 Inductors. The company wishes to make electronic goods using two circuits A and B. Requirement by circuit is as follows :

	Transistor	Capacitor	Inductor
A	175	300	200
B	125	100	300

The profit from circuit A and B is ₹2000 and ₹3000 respectively then constrains of the LLP based on this data are :

For the LPP Max Z=3x+4y, x+y≤40; x+2y≤ 60, x≥0, y≥0 the solution is:

The maximum value of\( z=2.5x+y\) subject to the constraints \( x+3y\leq12, 3x+y\leq12, x, y\geq0, \) is: 

The corner points of the feasible region determined by the system of linear inequalities are (0,0), (4, 0), (2, 4) and (0.5). If the maximum value of Z = ax + by where a, \(b > 0\) occurs at both (2, 4) and (4.0), then

Two tailors A and B earn ₹150 and ₹200 per day respectively. A can stitch 6 shirts and 4 pants per day, while B can stitch 10 shirts and 4 pants per day. If the tailors A and B work for x and y days respectively. To maximize the earning for producing at least 60 shirts and 32 pants, the LPP is:

For the LPP
Maximise z=x+y
subject to x-y≤-1, x+y≤2, x, y≥0, z has:

If objective function for LPP is\( z=5x+7y \)and corner points of feasible region are\( (0, 0) (7, 0) (3, 4)\) and\( (0, 2) \)then maximum value of \( z \) occurs at :
\((A) (0,0)\)
\((B) (7,0)\)
\((C) (3,4)\)
\((D) (0,2)\)
\((E) (4,3) \)
Choose the correct answer from the options given below:

Corners points of the feasible region for an LPP are \((1, 1)(2, 0) (3, 1)(\frac32,4)\) and \((0,5)\).Let \(z = px + 4y\),  be the objective function. If maximum of z occurs at \((\frac32,4)\) and\((3,1)\),then the value of p is : 
 

The maximum number of passengers an aeroplane can carry is 300. A profit of ₹1200 is made on each executive class ticket and a profit of ₹800 is made on each economy class ticket. The airline reserves atleast 40 seats for executive class. However, atleast 5 times as many passengers prefer to travel by economy class than by executive class. The maximum profit of the airline is:

The solution x₁ = 1, x₂ = 1, x₃ = 0 and z = 3 to the system of equations
x₁+x₂+x₃=2
x₁+x₂-x₃=2
x₁,x₂,x₃≥0
which minimizes z = x₁ + 2x₂ + 3x₃ is

Which of the following is false for linear programming problem (LLP)?

The maximum value of Z = x + 2y subjected to the constraints x+2y≥100, 2x-y≤0,2x + y≤ 200,x≥ 0, y≥0, is:

If there is no feasible region in LPP, then the problem has:

From the given system of constraints
A. 3x+5y≤90
B. x + 2y≤30
C. 2x + y≤30
D. x≥0, y≥0
The redundant constraint is :

The solution of the Linear Programming Problem
maximize Z = 107x + y
subject to constraints x + y ≤2
-3x + y ≥ 3
x, y ≥ 0 is

If \( A = \begin{bmatrix} 1 & -2 & 0 \\ 2 & -1 & -1 \\ 0 & -2 & 1 \end{bmatrix} \), find \( A^{-1} \) and use it to solve the following system of equations:

\[ x - 2y = 10, \quad 2x - y - z = 8, \quad -2y + z = 7. \]